Influence of self-steepening and intrapulse Raman scattering on modulation instability in oppositely directed coupler

We investigate the modulation instability in oppositely directed coupler in the presence of higher-order effects. Using linear stability analysis, we obtain an expression for instability gain. Special attention is paid to find out the influence of self-steepening effect and intrapulse Raman scattering on modulation instability. The study shows that in normal dispersion, regime instability gain exists even if perturbation frequency $\left(\Omega \right)$ is zero. But the instability gain at $\Omega =0$ is zero, when the dispersion is anomalous. Moreover, self-steepening effect and intrapulse Raman scattering form new instability regions and, hence, provide a new way to generate solitons or ultrashort pulses. Further, efficient control of modulation instability by adjusting self-steepening effect and intrapulse Raman scattering also successfully demonstrated.

Figure 1

Instability gain spectra in normal group velocity dispersion regime under different combinations of $s_1$ and $s_2$ when $p=10$ kW, and $k_{12}=k_{21}=10$ ${\text{m}}^{-1}$. (a) $s_1=0$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=0$ $\mathrm{ps}/\left(\mathrm{kWm}\right),$ (b) $s_1=0$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),$ (c) $s_1=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right)$ and (d) $s_1=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=-1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right).$

Figure 2

Instability gain spectra in anomalous group velocity dispersion regime under different combinations of $s_1$ and $s_2$ when $p=10$ $\text{kW}$, and $k_{12}=k_{21}=10$ ${\text{m}}^{-1}.$ (a) $s_1=0$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=0$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),$ (b) $s_1=0$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),$ (c) $s_1=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right)$ and (c) $s_1=1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),s_2=-1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right).$

Figure 3

Instability gain spectra showing the effect of intrapulse Raman scattering in (a) normal group velocity dispersion regime and (b) anomalous group velocity dispersion regime when $p=10$ $\text{kW}$, and $k_{12}=k_{21}=10$ ${\text{m}}^{-1},s_1=s_2=0$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right),$ and $T_{R1}=T_{R2}=0.1$ $\mathrm{ps}/\left(\mathrm{kW}\mathrm{m}\right)$.

Figure 4

Instability gain spectra showing the combined effect of self-steepening and intrapulse Raman scattering in (a) normal group velocity dispersion regime and (b) anomalous group velocity dispersion regime, when $p=10$ $\text{kW},k_{12}=k_{21}=10$ ${\text{m}}^{-1}$, and $s_1=s_2=1$ $\text{ps}/\left(\text{kW}\text{m}\right)$.